This invention relates to the control of adaptive optical elements, and more particularly to a method for the compensation of amplitude and phase fluctuations that result from the propagation of light through an extended turbulent medium.
Deformable mirrors have been used in recent years in astronomical telescopes to compensate for distortions of incident light caused by atmospheric turbulence. While the atmosphere distorts the wave front in both amplitude and phase, at the high angles that astronomical telescopes normally operate (within 60xc2x0 of zenith), only the phase fluctuations are significant. Both phase and amplitude fluctuations, however, are significant for lower elevation angles or for extended horizontal paths.
Conventional adaptive optical (AO) astronomical systems in use today employ only a single-phase correction device (nominally a conventional flexible thin facesheet deformable mirror) to compensate for the random phase fluctuations induced by propagation through a turbulent medium. This is partly due to the operation of telescopes at high elevation angles. It is also due to the fact that there currently exists no practical system to compensate for both phase and amplitude fluctuations. The use of a single-phase correction device imposes two fundamental limitations. First, the compensated field of view is limited to just slightly larger than the isoplanatic angle, "THgr"0. The compensated field of view is the angular extent over which the imaging performance of a telescope system is acceptable. This is typically defined to be the angle over which the Strehl ratio (a measure of imaging performance ranging from 0 to 1) is greater than xc2xd that achieved by a single deformable mirror adaptive optical system along the optical axis. The isoplanatic angle is a theoretical approximation of the compensated field of view associated with a single deformable mirror adaptive optical system. Atmospheric turbulence can limit this value to be quite small leading to poor imaging performance everywhere except a very narrow cone angle. Second, when light propagates through extended turbulence, whether due to a long horizontal path propagation or due to imaging or propagation at low elevation angles, the amplitude as well as phase fluctuations begin to significantly degrade the performance of an imaging or propagation system.
Past research has focused on mitigating each of these two major limitations following two fairly distinct paths. When the amplitude fluctuations are very weak and the geometric optics approximation is valid, the compensated field of view can be increased by use of multiple wavefront sensing beacons to form a tomographic estimate of the phase in the atmosphere. Then, the optimal commands to be applied to an arbitrary number of phase correction devices can be determined to maximize the compensated field of view. The advantages offered by this approach are that it can be implemented as a linear system, and it is a natural extension of the current state of the art. This approach is referred to as the classical multi-conjugate adaptive optics technique. Although this approach is quite mature and work is underway worldwide in the astronomy community to implement multi-conjugate adaptive optical systems, due to the use of the geometrical optics approximation inherent in its development, this approach only addressed the first limitation (the compensated field of view).
Research concerning the second limitation (propagation through extended turbulence leading to significant amplitude fluctuations) took a significantly different approach due to the fact that exactly when scintillation becomes such that it is worth attempting to compensate, the geometrical optics approximation is no longer valid. The need to incorporate wave optical propagation physics into the control algorithms led to the use of iterative vector space projection algorithms to determine the phase commands to be applied to the two deformable mirrors. The research in this area initially considered a phase correction device conjugate to the pupil and to the far field. More recently, a further improvement was found by placing the second phase correction device conjugate to a finite range. (Barchers, J. D. and B. L. Ellerbroek, Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments, Vol. 18, No. 2, J. Opt. Soc. Am. A, February 2001.) This early work utilized infinite resolution phase correction devices and wavefront sensors. The control algorithms were improved to handle finite resolution phase correction devices and wavefront sensors by augmenting spatial filtering techniques into the optimization process to prevent high spatial frequency propagation effects from corrupting the control commands. (Barchers, J. D., Evaluation of the impact of finite resolution effects on scintillation compensation using two deformable mirrors, accepted for publication in J. Opt. Soc. Am. A, 2001, and Barchers, J. D., Application of the parallel generalized projection algorithm to the control of two finite resolution deformable mirrors for scintillation compensation, accepted for publication in J. Opt. Soc. Am. A, 2001) Even more recently, the first control algorithm designed to simultaneously increase the compensated field of view and to compensate for amplitude as well as phase fluctuations was presented. (Barchers, J. D. and B. L. Ellerbroek, Increase in the compensated field of view in strong scintillation by use of two deformable mirrors, in Beyond Conventional Adaptive Optics, R. Ragazonni, Editor, May 2001.) While all of this work represents an important series of preliminary steps toward implementation of a multi-conjugate adaptive optical system to compensate for amplitude and phase fluctuations (and possibly even to increase the compensated field of view), there are two major difficulties that need to be overcome prior to proceeding towards implementation. The first limitation is that the algorithms that were studied for application in the strong scintillation regime are iterative and generally require 40-60 iterations to converge. Each individual iteration requires calculations comparable to a conventional adaptive optical system, however, the sum total represents a great increase in the required number of calculations over the current state of the art. This increase in the required computation time has served as an excuse to largely treat the use of multiple phase correction devices for scintillation compensation as an academic exercise: interesting but not very practical.
The second limitation of the iterative approaches is that their formulation requires an open-loop approach. The input wavefront corrupted by turbulence must be measured and the control commands then generated by software emulation of propagation physics. Such an approach requires nearly perfect calibration of the phase correction devices and wavefront sensors. It is also limited by the resolution at which the propagation physics can be emulated in software.
Neither an iterative calculation requiring many numerical calculations to be performed nor an open loop approach is desirable. Development of a sufficiently high-speed software architecture suitable for iterative calculations would be both costly and time consuming. An open loop approach is not desirable due to the fact that any uncertainties in the system (uncertain gains, misalignments, etc.) lead directly to reduced compensation whereas in a closed loop approach, some performance robustness to model uncertainties is preserved.
Accordingly, a closed-loop, or null-seeking, approach would be a significant improvement over the current open loop, iterative approaches as this would significantly reduce system complexity and greatly improve performance robustness.
In a preferred embodiment, the invention provides a means for controlling two phase correction devices that compensate for both amplitude and phase fluctuations resulting from propagation through a turbulent medium. By proper selection of a residual error signal, the technique implements open loop, iterative algorithms in a closed-loop stable fashion. In general, four wavefront sensing measurements are required: a measurement of the incoming beam at the plane of both phase correction devices and a measurement of the outgoing beam (either a real or artificially generated reference outgoing beam) at the plane of both phase correction devices. An embodiment that requires only two wavefront sensing measurements is possible if the wavefront sensing beacon is temporally coherent and is either a point source or, if an extended source, is spatially coherent. In either embodiment, the control loops associated with each phase correction device are decoupled. Furthermore, the required number of electronic calculations to be performed per phase correction device is no greater than that required for current conventional adaptive optical systems.
Other aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawing, illustrating by way of example the principles of the invention.